source: lemon-0.x/src/work/jacint/max_flow.h @ 478:8c74de352f80

// -*- C++ -*-

/*
Heuristics: 
 2 phase
 gap
 list 'level_list' on the nodes on level i implemented by hand
 stack 'active' on the active nodes on level i
 runs heuristic 'highest label' for H1*n relabels
 runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
 
Parameters H0 and H1 are initialized to 20 and 1.

Constructors:

Preflow(Graph, Node, Node, CapMap, FlowMap, bool) : bool must be false if 
     FlowMap is not constant zero, and should be true if it is

Members:

void run()

Num flowValue() : returns the value of a maximum flow

void minMinCut(CutMap& M) : sets M to the characteristic vector of the 
     minimum min cut. M should be a map of bools initialized to false. ??Is it OK?

void maxMinCut(CutMap& M) : sets M to the characteristic vector of the 
     maximum min cut. M should be a map of bools initialized to false.

void minCut(CutMap& M) : sets M to the characteristic vector of 
     a min cut. M should be a map of bools initialized to false.

*/

#ifndef HUGO_PREFLOW_H
#define HUGO_PREFLOW_H

#define H0 20
#define H1 1

#include <vector>
#include <queue>
#include <stack>

#include <graph_wrapper.h>
#include <bfs_iterator.h>
#include <invalid.h>
#include <maps.h>
#include <for_each_macros.h>


namespace hugo {

  template <typename Graph, typename Num, 
            typename CapMap=typename Graph::template EdgeMap<Num>, 
            typename FlowMap=typename Graph::template EdgeMap<Num> >
  class MaxFlow {
    
    typedef typename Graph::Node Node;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;

    typedef typename std::vector<std::stack<Node> > VecStack;
    typedef typename Graph::template NodeMap<Node> NNMap;
    typedef typename std::vector<Node> VecNode;

    const Graph* g;
    Node s;
    Node t;
    const CapMap* capacity;  
    FlowMap* flow;
    int n;      //the number of nodes of G
    typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
    typedef typename ResGW::Edge ResGWEdge;
    //typedef typename ResGW::template NodeMap<bool> ReachedMap;
    typedef typename Graph::template NodeMap<int> ReachedMap;
    ReachedMap level;
    //level works as a bool map in augmenting path algorithms 
    //and is used by bfs for storing reached information.
    //In preflow, it shows levels of nodes.
    //typename Graph::template NodeMap<int> level;    
    typename Graph::template NodeMap<Num> excess; 

  public:
 
    enum flowEnum{
      ZERO_FLOW=0,
      GEN_FLOW=1,
      PREFLOW=2
    };

    MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, 
            FlowMap& _flow) :
      g(&_G), s(_s), t(_t), capacity(&_capacity), 
      flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {}

    void run() {
      preflow( ZERO_FLOW );
    }
    
    void preflow( flowEnum fe ) {
      preflowPhase0(fe);
      preflowPhase1();
    }

    void preflowPhase0( flowEnum fe );

    void preflowPhase1();

    bool augmentOnShortestPath();

    template<typename MutableGraph> bool augmentOnBlockingFlow();

    bool augmentOnBlockingFlow2();

    /// Returns the actual flow value.
    /// More precisely, it returns the negative excess of s, thus 
    /// this works also for preflows.
    Num flowValue() { 
      Num a=0;
      FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e];
      FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e];
      return a;
    }

    //should be used only between preflowPhase0 and preflowPhase1
    template<typename _CutMap>
    void actMinCut(_CutMap& M) {
      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) 
      if ( level[v] < n ) {
        M.set(v,false);
      } else {
        M.set(v,true);
      }
    }



    /*
      Returns the minimum min cut, by a bfs from s in the residual graph.
    */
    template<typename _CutMap>
    void minMinCut(_CutMap& M) {
    
      std::queue<Node> queue;
      
      M.set(s,true);      
      queue.push(s);

      while (!queue.empty()) {
        Node w=queue.front();
        queue.pop();

        OutEdgeIt e;
        for(g->first(e,w) ; g->valid(e); g->next(e)) {
          Node v=g->head(e);
          if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
            queue.push(v);
            M.set(v, true);
          }
        } 

        InEdgeIt f;
        for(g->first(f,w) ; g->valid(f); g->next(f)) {
          Node v=g->tail(f);
          if (!M[v] && (*flow)[f] > 0 ) {
            queue.push(v);
            M.set(v, true);
          }
        } 
      }
    }


  
    /*
      Returns the maximum min cut, by a reverse bfs 
      from t in the residual graph.
    */
    
    template<typename _CutMap>
    void maxMinCut(_CutMap& M) {

      NodeIt v;
      for(g->first(v) ; g->valid(v); g->next(v)) {
        M.set(v, true);
      }

      std::queue<Node> queue;
      
      M.set(t,false);        
      queue.push(t);

      while (!queue.empty()) {
        Node w=queue.front();
        queue.pop();


        InEdgeIt e;
        for(g->first(e,w) ; g->valid(e); g->next(e)) {
          Node v=g->tail(e);
          if (M[v] && (*flow)[e] < (*capacity)[e] ) {
            queue.push(v);
            M.set(v, false);
          }
        }
        
        OutEdgeIt f;
        for(g->first(f,w) ; g->valid(f); g->next(f)) {
          Node v=g->head(f);
          if (M[v] && (*flow)[f] > 0 ) {
            queue.push(v);
            M.set(v, false);
          }
        }
      }
    }


    template<typename CutMap>
    void minCut(CutMap& M) {
      minMinCut(M);
    }

    void resetTarget(Node _t) {t=_t;}
    void resetSource(Node _s) {s=_s;}
   
    void resetCap(const CapMap& _cap) {
      capacity=&_cap;
    }
    
    void resetFlow(FlowMap& _flow) {
      flow=&_flow;
    }


  private:

    int push(Node w, VecStack& active) {
      
      int lev=level[w];
      Num exc=excess[w];
      int newlevel=n;       //bound on the next level of w
          
      OutEdgeIt e;
      for(g->first(e,w); g->valid(e); g->next(e)) {
            
        if ( (*flow)[e] >= (*capacity)[e] ) continue; 
        Node v=g->head(e);            
            
        if( lev > level[v] ) { //Push is allowed now
          
          if ( excess[v]<=0 && v!=t && v!=s ) {
            int lev_v=level[v];
            active[lev_v].push(v);
          }
          
          Num cap=(*capacity)[e];
          Num flo=(*flow)[e];
          Num remcap=cap-flo;
          
          if ( remcap >= exc ) { //A nonsaturating push.
            
            flow->set(e, flo+exc);
            excess.set(v, excess[v]+exc);
            exc=0;
            break; 
            
          } else { //A saturating push.
            flow->set(e, cap);
            excess.set(v, excess[v]+remcap);
            exc-=remcap;
          }
        } else if ( newlevel > level[v] ) newlevel = level[v];
      } //for out edges wv 
      
      if ( exc > 0 ) {  
        InEdgeIt e;
        for(g->first(e,w); g->valid(e); g->next(e)) {
          
          if( (*flow)[e] <= 0 ) continue; 
          Node v=g->tail(e); 
          
          if( lev > level[v] ) { //Push is allowed now
            
            if ( excess[v]<=0 && v!=t && v!=s ) {
              int lev_v=level[v];
              active[lev_v].push(v);
            }
            
            Num flo=(*flow)[e];
            
            if ( flo >= exc ) { //A nonsaturating push.
              
              flow->set(e, flo-exc);
              excess.set(v, excess[v]+exc);
              exc=0;
              break; 
            } else {  //A saturating push.
              
              excess.set(v, excess[v]+flo);
              exc-=flo;
              flow->set(e,0);
            }  
          } else if ( newlevel > level[v] ) newlevel = level[v];
        } //for in edges vw
        
      } // if w still has excess after the out edge for cycle
      
      excess.set(w, exc);
      
      return newlevel;
     }


    void preflowPreproc ( flowEnum fe, VecStack& active, 
                          VecNode& level_list, NNMap& left, NNMap& right ) {

      std::queue<Node> bfs_queue;
      
      switch ( fe ) {
      case ZERO_FLOW: 
        {
          //Reverse_bfs from t, to find the starting level.
          level.set(t,0);
          bfs_queue.push(t);
        
          while (!bfs_queue.empty()) {
            
            Node v=bfs_queue.front();   
            bfs_queue.pop();
            int l=level[v]+1;
            
            InEdgeIt e;
            for(g->first(e,v); g->valid(e); g->next(e)) {
              Node w=g->tail(e);
              if ( level[w] == n && w != s ) {
                bfs_queue.push(w);
                Node first=level_list[l];
                if ( g->valid(first) ) left.set(first,w);
                right.set(w,first);
                level_list[l]=w;
                level.set(w, l);
              }
            }
          }
          
          //the starting flow
          OutEdgeIt e;
          for(g->first(e,s); g->valid(e); g->next(e)) 
            {
              Num c=(*capacity)[e];
              if ( c <= 0 ) continue;
              Node w=g->head(e);
              if ( level[w] < n ) {       
                if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
                flow->set(e, c); 
                excess.set(w, excess[w]+c);
              }
            }
          break;
        }
        
      case GEN_FLOW:
      case PREFLOW:
        {
          //Reverse_bfs from t in the residual graph, 
          //to find the starting level.
          level.set(t,0);
          bfs_queue.push(t);
          
          while (!bfs_queue.empty()) {
            
            Node v=bfs_queue.front();   
            bfs_queue.pop();
            int l=level[v]+1;
            
            InEdgeIt e;
            for(g->first(e,v); g->valid(e); g->next(e)) {
              if ( (*capacity)[e] <= (*flow)[e] ) continue;
              Node w=g->tail(e);
              if ( level[w] == n && w != s ) {
                bfs_queue.push(w);
                Node first=level_list[l];
                if ( g->valid(first) ) left.set(first,w);
                right.set(w,first);
                level_list[l]=w;
                level.set(w, l);
              }
            }
            
            OutEdgeIt f;
            for(g->first(f,v); g->valid(f); g->next(f)) {
              if ( 0 >= (*flow)[f] ) continue;
              Node w=g->head(f);
              if ( level[w] == n && w != s ) {
                bfs_queue.push(w);
                Node first=level_list[l];
                if ( g->valid(first) ) left.set(first,w);
                right.set(w,first);
                level_list[l]=w;
                level.set(w, l);
              }
            }
          }
          
          
          //the starting flow
          OutEdgeIt e;
          for(g->first(e,s); g->valid(e); g->next(e)) 
            {
              Num rem=(*capacity)[e]-(*flow)[e];
              if ( rem <= 0 ) continue;
              Node w=g->head(e);
              if ( level[w] < n ) {       
                if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
                flow->set(e, (*capacity)[e]); 
                excess.set(w, excess[w]+rem);
              }
            }
          
          InEdgeIt f;
          for(g->first(f,s); g->valid(f); g->next(f)) 
            {
              if ( (*flow)[f] <= 0 ) continue;
              Node w=g->tail(f);
              if ( level[w] < n ) {       
                if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
                excess.set(w, excess[w]+(*flow)[f]);
                flow->set(f, 0); 
              }
            }  
          break;
        } //case PREFLOW
      }
    } //preflowPreproc



    void relabel(Node w, int newlevel, VecStack& active,  
                 VecNode& level_list, NNMap& left, 
                 NNMap& right, int& b, int& k, bool what_heur ) 
    {

      Num lev=level[w]; 
      
      Node right_n=right[w];
      Node left_n=left[w];
      
      //unlacing starts
      if ( g->valid(right_n) ) {
        if ( g->valid(left_n) ) {
          right.set(left_n, right_n);
          left.set(right_n, left_n);
        } else {
          level_list[lev]=right_n;   
          left.set(right_n, INVALID);
        } 
      } else {
        if ( g->valid(left_n) ) {
          right.set(left_n, INVALID);
        } else { 
          level_list[lev]=INVALID;   
        } 
      } 
      //unlacing ends
                
      if ( !g->valid(level_list[lev]) ) {
              
        //gapping starts
        for (int i=lev; i!=k ; ) {
          Node v=level_list[++i];
          while ( g->valid(v) ) {
            level.set(v,n);
            v=right[v];
          }
          level_list[i]=INVALID;
          if ( !what_heur ) {
            while ( !active[i].empty() ) {
              active[i].pop();    //FIXME: ezt szebben kene
            }
          }          
        }
        
        level.set(w,n);
        b=lev-1;
        k=b;
        //gapping ends
        
      } else {
        
        if ( newlevel == n ) level.set(w,n); 
        else {
          level.set(w,++newlevel);
          active[newlevel].push(w);
          if ( what_heur ) b=newlevel;
          if ( k < newlevel ) ++k;      //now k=newlevel
          Node first=level_list[newlevel];
          if ( g->valid(first) ) left.set(first,w);
          right.set(w,first);
          left.set(w,INVALID);
          level_list[newlevel]=w;
        }
      }
      
    } //relabel


    template<typename MapGraphWrapper> 
    class DistanceMap {
    protected:
      const MapGraphWrapper* g;
      typename MapGraphWrapper::template NodeMap<int> dist; 
    public:
      DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }
      void set(const typename MapGraphWrapper::Node& n, int a) { 
        dist.set(n, a); 
      }
      int operator[](const typename MapGraphWrapper::Node& n) 
        { return dist[n]; }
//       int get(const typename MapGraphWrapper::Node& n) const { 
//      return dist[n]; }
//       bool get(const typename MapGraphWrapper::Edge& e) const { 
//      return (dist.get(g->tail(e))<dist.get(g->head(e))); }
      bool operator[](const typename MapGraphWrapper::Edge& e) const { 
        return (dist[g->tail(e)]<dist[g->head(e)]); 
      }
    };
    
  };


  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase0( flowEnum fe ) 
  {
      
      int heur0=(int)(H0*n);  //time while running 'bound decrease' 
      int heur1=(int)(H1*n);  //time while running 'highest label'
      int heur=heur1;         //starting time interval (#of relabels)
      int numrelabel=0;
     
      bool what_heur=1;       
      //It is 0 in case 'bound decrease' and 1 in case 'highest label'

      bool end=false;     
      //Needed for 'bound decrease', true means no active nodes are above bound b.

      int k=n-2;  //bound on the highest level under n containing a node
      int b=k;    //bound on the highest level under n of an active node
      
      VecStack active(n);
      
      NNMap left(*g, INVALID);
      NNMap right(*g, INVALID);
      VecNode level_list(n,INVALID);
      //List of the nodes in level i<n, set to n.

      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
      //setting each node to level n
      
      switch ( fe ) {
      case PREFLOW:
        {
          //counting the excess
          NodeIt v;
          for(g->first(v); g->valid(v); g->next(v)) {
            Num exc=0;
          
            InEdgeIt e;
            for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e];
            OutEdgeIt f;
            for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f];
            
            excess.set(v,exc);    
            
            //putting the active nodes into the stack
            int lev=level[v];
            if ( exc > 0 && lev < n && v != t ) active[lev].push(v);
          }
          break;
        }
      case GEN_FLOW:
        {
          //Counting the excess of t
          Num exc=0;
          
          InEdgeIt e;
          for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
          OutEdgeIt f;
          for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
          
          excess.set(t,exc);    
          
          break;
        }
      default:
        break;
      }
      
      preflowPreproc( fe, active, level_list, left, right );
      //End of preprocessing 
      
      
      //Push/relabel on the highest level active nodes.
      while ( true ) {
        if ( b == 0 ) {
          if ( !what_heur && !end && k > 0 ) {
            b=k;
            end=true;
          } else break;
        }
        
        if ( active[b].empty() ) --b; 
        else {
          end=false;  
          Node w=active[b].top();
          active[b].pop();
          int newlevel=push(w,active);
          if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, 
                                       left, right, b, k, what_heur);
          
          ++numrelabel; 
          if ( numrelabel >= heur ) {
            numrelabel=0;
            if ( what_heur ) {
              what_heur=0;
              heur=heur0;
              end=false;
            } else {
              what_heur=1;
              heur=heur1;
              b=k; 
            }
          }
        } 
      } 
    }



  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1() 
  {
      
      int k=n-2;  //bound on the highest level under n containing a node
      int b=k;    //bound on the highest level under n of an active node
      
      VecStack active(n);
      level.set(s,0);
      std::queue<Node> bfs_queue;
      bfs_queue.push(s);
            
      while (!bfs_queue.empty()) {
        
        Node v=bfs_queue.front();       
        bfs_queue.pop();
        int l=level[v]+1;
              
        InEdgeIt e;
        for(g->first(e,v); g->valid(e); g->next(e)) {
          if ( (*capacity)[e] <= (*flow)[e] ) continue;
          Node u=g->tail(e);
          if ( level[u] >= n ) { 
            bfs_queue.push(u);
            level.set(u, l);
            if ( excess[u] > 0 ) active[l].push(u);
          }
        }
        
        OutEdgeIt f;
        for(g->first(f,v); g->valid(f); g->next(f)) {
          if ( 0 >= (*flow)[f] ) continue;
          Node u=g->head(f);
          if ( level[u] >= n ) { 
            bfs_queue.push(u);
            level.set(u, l);
            if ( excess[u] > 0 ) active[l].push(u);
          }
        }
      }
      b=n-2;

      while ( true ) {
        
        if ( b == 0 ) break;

        if ( active[b].empty() ) --b; 
        else {
          Node w=active[b].top();
          active[b].pop();
          int newlevel=push(w,active);    

          //relabel
          if ( excess[w] > 0 ) {
            level.set(w,++newlevel);
            active[newlevel].push(w);
            b=newlevel;
          }
        }  // if stack[b] is nonempty
      } // while(true)
    }



  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() 
  {
      ResGW res_graph(*g, *capacity, *flow);
      bool _augment=false;
      
      //ReachedMap level(res_graph);
      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
      bfs.pushAndSetReached(s);
        
      typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); 
      pred.set(s, INVALID);
      
      typename ResGW::template NodeMap<Num> free(res_graph);
        
      //searching for augmenting path
      while ( !bfs.finished() ) { 
        ResGWOutEdgeIt e=bfs;
        if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
          Node v=res_graph.tail(e);
          Node w=res_graph.head(e);
          pred.set(w, e);
          if (res_graph.valid(pred[v])) {
            free.set(w, std::min(free[v], res_graph.resCap(e)));
          } else {
            free.set(w, res_graph.resCap(e)); 
          }
          if (res_graph.head(e)==t) { _augment=true; break; }
        }
        
        ++bfs;
      } //end of searching augmenting path

      if (_augment) {
        Node n=t;
        Num augment_value=free[t];
        while (res_graph.valid(pred[n])) { 
          ResGWEdge e=pred[n];
          res_graph.augment(e, augment_value); 
          n=res_graph.tail(e);
        }
      }

      return _augment;
    }









  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  template<typename MutableGraph> 
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() 
  {      
      typedef MutableGraph MG;
      bool _augment=false;

      ResGW res_graph(*g, *capacity, *flow);

      //bfs for distances on the residual graph
      //ReachedMap level(res_graph);
      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
      bfs.pushAndSetReached(s);
      typename ResGW::template NodeMap<int> 
        dist(res_graph); //filled up with 0's

      //F will contain the physical copy of the residual graph
      //with the set of edges which are on shortest paths
      MG F;
      typename ResGW::template NodeMap<typename MG::Node> 
        res_graph_to_F(res_graph);
      {
        typename ResGW::NodeIt n;
        for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
          res_graph_to_F.set(n, F.addNode());
        }
      }

      typename MG::Node sF=res_graph_to_F[s];
      typename MG::Node tF=res_graph_to_F[t];
      typename MG::template EdgeMap<ResGWEdge> original_edge(F);
      typename MG::template EdgeMap<Num> residual_capacity(F);

      while ( !bfs.finished() ) { 
        ResGWOutEdgeIt e=bfs;
        if (res_graph.valid(e)) {
          if (bfs.isBNodeNewlyReached()) {
            dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
            typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
            original_edge.update();
            original_edge.set(f, e);
            residual_capacity.update();
            residual_capacity.set(f, res_graph.resCap(e));
          } else {
            if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
              typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
              original_edge.update();
              original_edge.set(f, e);
              residual_capacity.update();
              residual_capacity.set(f, res_graph.resCap(e));
            }
          }
        }
        ++bfs;
      } //computing distances from s in the residual graph

      bool __augment=true;

      while (__augment) {
        __augment=false;
        //computing blocking flow with dfs
        DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
        typename MG::template NodeMap<typename MG::Edge> pred(F);
        pred.set(sF, INVALID);
        //invalid iterators for sources

        typename MG::template NodeMap<Num> free(F);

        dfs.pushAndSetReached(sF);      
        while (!dfs.finished()) {
          ++dfs;
          if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {
            if (dfs.isBNodeNewlyReached()) {
              typename MG::Node v=F.aNode(dfs);
              typename MG::Node w=F.bNode(dfs);
              pred.set(w, dfs);
              if (F.valid(pred[v])) {
                free.set(w, std::min(free[v], residual_capacity[dfs]));
              } else {
                free.set(w, residual_capacity[dfs]); 
              }
              if (w==tF) { 
                __augment=true; 
                _augment=true;
                break; 
              }
              
            } else {
              F.erase(/*typename MG::OutEdgeIt*/(dfs));
            }
          } 
        }

        if (__augment) {
          typename MG::Node n=tF;
          Num augment_value=free[tF];
          while (F.valid(pred[n])) { 
            typename MG::Edge e=pred[n];
            res_graph.augment(original_edge[e], augment_value); 
            n=F.tail(e);
            if (residual_capacity[e]==augment_value) 
              F.erase(e); 
            else 
              residual_capacity.set(e, residual_capacity[e]-augment_value);
          }
        }
        
      }
            
      return _augment;
    }






  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() 
  {
      bool _augment=false;

      ResGW res_graph(*g, *capacity, *flow);
      
      //ReachedMap level(res_graph);
      FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
      BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

      bfs.pushAndSetReached(s);
      DistanceMap<ResGW> dist(res_graph);
      while ( !bfs.finished() ) { 
        ResGWOutEdgeIt e=bfs;
        if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
          dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
        }
        ++bfs;
      } //computing distances from s in the residual graph

      //Subgraph containing the edges on some shortest paths
      ConstMap<typename ResGW::Node, bool> true_map(true);
      typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 
        DistanceMap<ResGW> > FilterResGW;
      FilterResGW filter_res_graph(res_graph, true_map, dist);

      //Subgraph, which is able to delete edges which are already 
      //met by the dfs
      typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> 
        first_out_edges(filter_res_graph);
      typename FilterResGW::NodeIt v;
      for(filter_res_graph.first(v); filter_res_graph.valid(v); 
          filter_res_graph.next(v)) 
      {
        typename FilterResGW::OutEdgeIt e;
        filter_res_graph.first(e, v);
        first_out_edges.set(v, e);
      }
      typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
        template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;
      ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);

      bool __augment=true;

      while (__augment) {

        __augment=false;
        //computing blocking flow with dfs
        DfsIterator< ErasingResGW, 
          typename ErasingResGW::template NodeMap<bool> > 
          dfs(erasing_res_graph);
        typename ErasingResGW::
          template NodeMap<typename ErasingResGW::OutEdgeIt> 
          pred(erasing_res_graph); 
        pred.set(s, INVALID);
        //invalid iterators for sources

        typename ErasingResGW::template NodeMap<Num> 
          free1(erasing_res_graph);

        dfs.pushAndSetReached(
          typename ErasingResGW::Node(
            typename FilterResGW::Node(
              typename ResGW::Node(s)
              )
            )
          );
        while (!dfs.finished()) {
          ++dfs;
          if (erasing_res_graph.valid(
                typename ErasingResGW::OutEdgeIt(dfs))) 
          { 
            if (dfs.isBNodeNewlyReached()) {
          
              typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);
              typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);

              pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));
              if (erasing_res_graph.valid(pred[v])) {
                free1.set(w, std::min(free1[v], res_graph.resCap(
                                       typename ErasingResGW::OutEdgeIt(dfs))));
              } else {
                free1.set(w, res_graph.resCap(
                           typename ErasingResGW::OutEdgeIt(dfs))); 
              }
              
              if (w==t) { 
                __augment=true; 
                _augment=true;
                break; 
              }
            } else {
              erasing_res_graph.erase(dfs);
            }
          }
        }       

        if (__augment) {
          typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t));
//        typename ResGW::NodeMap<Num> a(res_graph);
//        typename ResGW::Node b;
//        Num j=a[b];
//        typename FilterResGW::NodeMap<Num> a1(filter_res_graph);
//        typename FilterResGW::Node b1;
//        Num j1=a1[b1];
//        typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph);
//        typename ErasingResGW::Node b2;
//        Num j2=a2[b2];
          Num augment_value=free1[n];
          while (erasing_res_graph.valid(pred[n])) { 
            typename ErasingResGW::OutEdgeIt e=pred[n];
            res_graph.augment(e, augment_value);
            n=erasing_res_graph.tail(e);
            if (res_graph.resCap(e)==0)
              erasing_res_graph.erase(e);
        }
      }
      
      } //while (__augment) 
            
      return _augment;
    }




} //namespace hugo

#endif //HUGO_PREFLOW_H